Efficient sequential estimation for compound poisson processes

Abstract

This paper discusses uniformly minimum variance, unbiased sequential estimation of a real-valued parametric function for a compound Poisson process when the compounding random variables belong to the exponential family. The characterization of Cramer-Rao efficient plans by Stefanov (1982 b) is shown to be incomplete by obtaining a new efficient plan for the compound Poisson-Bernoulli process. This new plan completes the characterization of Cramer-Rao efficient plans. The class of Bhattacharyya efficient estimators of order two is determined for all the efficient sampling schemes.

Keywords:

• cramer-Rao and Bhattacharyya efficient estimation
• efficient Markov times
• exponential family

^∗This work was carried out when the first author (SRA) was visiting Miami University during 1985-86.

^∗This work was carried out when the first author (SRA) was visiting Miami University during 1985-86.

Notes

^∗This work was carried out when the first author (SRA) was visiting Miami University during 1985-86.